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<title>Atlas software user guide -- Structure theory</title>
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<h2>Structure theory</h2>
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<i>Last updated: October 15, 2005</i>
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The first main goal of the Atlas software package is to make available all
the structural data about reductive groups that is required for representation
theory. Let G be a connected complex reductive algebraic group, with a fixed 
chosen <a href="innerclass.html">inner class.</a> The following structural data
are currently available for G :
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the computation of the <a href="components.html">component group</a> of
any real form of G;
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the classification of <a href="realforms.html">weak</a> and
<a href="strongreal.html">strong</a> real forms for G;
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the classification of conjugacy classes of <a href="cartan.html">Cartan 
subgroups</a> of G;
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the computation of the <a href="realweyl.html">real Weyl group</a> 
corresponding to each Cartan subgroup;
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the classification of <a href="kgb.html">the K-orbits in G &#8260; B</a>;
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It should be stressed that all this information is computed, not looked up
in databases. The only input that the program requires is the
<a href="rootdata.html">root datum</a> for G (which is constructed during
the initial user interaction), and the choice of inner class.
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<a href="userintro.html">Back</a> to the introduction.<br>
<a href="http://atlas.math.umd.edu">Back</a> to the Atlas homepage.
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